Deformation Spaces of Hyperbolic 3-manifolds
双曲3流形的变形空间
基本信息
- 批准号:0406976
- 负责人:
- 金额:$ 8.67万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2003
- 资助国家:美国
- 起止时间:2003-07-01 至 2006-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
DMS-0204763Kenneth BrombergThe investigator plans to study spaces of hyperbolic metrics on a fixed3-manifold. Unlike on a closed manifold, on an open 3-manifold there willtypically be a large space of hyperbolic metrics. The investigatorsgoal is to understand this space. Some questions are simple to state:Is the deformation space the closure of its interior? A more detaileddescription of the space is the ending lamination conjecture,which gives invariants that classify every hyperbolic metric onthe manifold. This classification is not a parameterization; the map tothe space of invariants is not continuous. The investigator isinterested in understanding these discontinuities and describing thetopology of the deformation space of metrics. Hyperbolic cone-metricsare a key tool used throughout this work. The philosophy is that verycomplicated geometry in a smooth hyperbolic structure can be exchangedfor a less complicated, but singular, hyperbolic cone metric.Three manifolds are mathematical spaces that locally look like theuniverse we live in. Mathematicians, beginning with Poincare, have beeninterested in classification question about three manifolds. Hyperbolicgeometry is also a very old field dating back to the middle of theeighteenth century. In the last twenty-five years, largely due to the workThurston, it has been realized that there are deep and beautifulconnections between the two topics.
DMS-0204763Kenneth Bromberg 研究人员计划研究固定 3 流形上的双曲度量空间。与闭流形不同,在开三流形上通常会有很大的双曲度量空间。调查人员的目标是了解这个空间。有些问题很容易表述:变形空间是其内部的封闭吗?对空间的更详细描述是最终层压猜想,它给出了对流形上的每个双曲度量进行分类的不变量。这种分类不是参数化;而是参数化。不变量空间的映射不是连续的。研究人员有兴趣了解这些不连续性并描述度量变形空间的拓扑。双曲锥度量是整个工作中使用的关键工具。其理念是,平滑双曲结构中非常复杂的几何形状可以替换为不太复杂但奇异的双曲圆锥度量。三流形是局部看起来像我们生活的宇宙的数学空间。从庞加莱开始,数学家一直对三流形的分类问题感兴趣。双曲几何也是一个非常古老的领域,其历史可以追溯到十八世纪中叶。在过去的二十五年里,很大程度上由于瑟斯顿的工作,人们已经意识到这两个主题之间存在着深刻而美丽的联系。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Kenneth Bromberg其他文献
Tameness on the boundary and Ahlfors’ measure conjecture
- DOI:
10.1007/s10240-003-0018-y - 发表时间:
2003-12-01 - 期刊:
- 影响因子:3.500
- 作者:
Jeffrey Brock;Kenneth Bromberg;Richard Evans;Juan Souto - 通讯作者:
Juan Souto
emL/emsup2/sup-bounds for drilling short geodesics in convex co-compact hyperbolic 3-manifolds
凸共紧双曲 3 维流形中短测地线钻探的 emL/emsup2/sup 界
- DOI:
10.1016/j.aim.2024.109804 - 发表时间:
2024-08-01 - 期刊:
- 影响因子:1.500
- 作者:
Martin Bridgeman;Kenneth Bromberg - 通讯作者:
Kenneth Bromberg
Pneumococcal C and type polysaccharide detection in the concentrated urine of patients with bacteremia
- DOI:
10.1007/bf00189611 - 发表时间:
1990-12-01 - 期刊:
- 影响因子:3.000
- 作者:
Kenneth Bromberg;Gaylene Tannis;Alma Rodgers - 通讯作者:
Alma Rodgers
Congenital syphilis: detection of Treponema pallidum in stillborns.
先天性梅毒:死产中梅毒螺旋体的检测。
- DOI:
10.1093/clinids/24.1.24 - 发表时间:
1997 - 期刊:
- 影响因子:0
- 作者:
S. Rawstron;J. Vetrano;G. Tannis;Kenneth Bromberg - 通讯作者:
Kenneth Bromberg
LYMPHOCYTE POPULATION AND FUNCTION IN PERTUSSIS
百日咳中淋巴细胞群体和功能
- DOI:
10.1203/00006450-198404001-00996 - 发表时间:
1984-04-01 - 期刊:
- 影响因子:3.100
- 作者:
Edward Kong;Senih M Fikrig;Rajendra N Pahwa;Kenneth Bromberg - 通讯作者:
Kenneth Bromberg
Kenneth Bromberg的其他文献
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{{ truncateString('Kenneth Bromberg', 18)}}的其他基金
Hyperbolic Geometry and the Mapping Class Group
双曲几何和映射类组
- 批准号:
1906095 - 财政年份:2019
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
Conference on Aspects of Non-Positive and Negative Curvature in Group Theory
群论中非正曲率和负曲率方面的会议
- 批准号:
1856388 - 财政年份:2019
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
International Conference in Geometric Topology
几何拓扑国际会议
- 批准号:
1719746 - 财政年份:2017
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
Hyperbolic geometry and mapping class groups
双曲几何和映射类组
- 批准号:
1509171 - 财政年份:2015
- 资助金额:
$ 8.67万 - 项目类别:
Continuing Grant
RTG: Algebraic Geometry and Topology at the University of Utah
RTG:犹他大学代数几何和拓扑
- 批准号:
1246989 - 财政年份:2013
- 资助金额:
$ 8.67万 - 项目类别:
Continuing Grant
Conference Proposal - Rigidity and Flexibility in Dimensions 2, 3 and 4
会议提案——维度2、3、4的刚性和灵活性
- 批准号:
1211355 - 财政年份:2012
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
Research in hyperbolic geometry and mapping class groups
双曲几何与映射类群研究
- 批准号:
1207873 - 财政年份:2012
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
Hyperbolic geometry in dimensions 2 and 3
2 维和 3 维双曲几何
- 批准号:
0906118 - 财政年份:2009
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
Focused Research Group: Collaborative Research: Geometry and Deformation Theory of Hyperbolic 3-Manifolds
重点研究组:合作研究:双曲3流形的几何与变形理论
- 批准号:
0554569 - 财政年份:2006
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
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